Mathematics Curriculum Standards Research Articles

A Study on the Application of Task-Driven Teaching Method in High School Mathematics Teaching: Taking “The Determination of Vertical Line and Plane” as an Example

The “Ordinary High School Mathematics Curriculum Standards (2017 Edition, 2020 Revision)” clearly stated in “Teaching Suggestions” that “teaching activities based on the core literacy of mathematics should grasp the essence of mathematics, create appropriate teaching situations, put forward appropriate mathematical questions, stimulate students to think and communicate, and form and develop the core literacy of mathematics.” The task-driven teaching model is a new type of teaching method that takes tasks as the main line, teachers as the guide, and students as the main body, which can enable students to engage deeply in classroom discussions and think actively. Based on the characteristics and principles of the task-driven teaching method, this paper designs a high school mathematics classroom teaching based on the task-driven teaching method, hoping to provide a reference for the majority of front-line teachers.

Research on the Use Power Point (PPT) in Junior High School Mathematics Classroom Teaching

Since PowerPoint (hereinafter referred to as PPT) is of great significance to mathematics teaching, more and more attention has been paid to how to use PPT effectively in junior high school mathematics classroom teaching. This paper uses the method of theoretical analysis, through the analysis of the characteristics of PPT, the current teaching situation and the problems existing in students' mathematics learning, combined with the various requirements of the Mathematics Curriculum Standards for Compulsory Education (2022 Edition) (hereinafter referred to as The Standards) for junior high school mathematics teaching, puts forward four strategies for using PPT in junior high school mathematics classroom teaching. Through analysis, we can know that PPT is characterized by its powerful presentation function, dynamic presentation effect, lacks of procedural presentation, multiple ways of emphasis, and strong inclusiveness. The current problem of students in mathematics learning is students do not have a firm grasp of basic knowledge and have an inaccurate understanding of many concepts, students' ability to analyze and solve mathematical problems is weak, and they cannot accurately understand the conditions and requirements of the problems, students lack enthusiasm for learning mathematics, and students have improper learning methods and lack the habit of writing on time. The current situation of mathematics classroom teaching is teachers pay too much attention to the teaching of problem-solving methods and calculations and neglect the inspiration and training of problem-solving ideas, teachers' teaching resources are obsolete, and the use of information technology in teaching is inadequate, teachers' teaching methods are rigid and lack diversity and innovation, and the interaction between teachers and students is mostly ineffective and the overall participation of students is low. The standard puts forward specific requirements for the teaching of number and algebra, graphics and geometry, statistics and probability in junior high school. Therefore, through the above analysis, we give the following suggestions: 1. Making full use of the multiple emphasis effect of PPT to highlight different mathematical symbols; 2. Skillfully using the dynamic presentation function of PPT to make the process of mathematical knowledge formation dynamic; 3. Expanding the scope of use of PPT and give full play to the value of PPT in all aspects of teaching; 4. Integrating and collocating a variety of technologies reasonably, and use PPT in a variety of ways to teach mathematics. These strategies can be used for reference by junior high school mathematics teachers in practical teaching.

Core competency oriented problem-solving teaching ----Taking "Solving Application Problems with a System of Equations" as an Example

The teaching of Mathematical problem-solving is one of the three key teaching points in junior high school mathematics. Solving applied problems through equations (systems) is an important component of the first module of teaching content, "Numbers and Algebra", and holds a very important position. It is a key focus in junior high school mathematics problem-solving teaching. At present, under the premise of the implementation of the new curriculum reform in the field of mathematics in China, based on the recent publication of compulsory education curriculum standards,the teachers of mathematics should focus on cultivating excellent mathematical core literacy among junior high school students, and ensuring that they can independently cope with and solve problems in the math teaching of junior high school. Based on the above background, the author focuses on the newly published mathematics curriculum standards in 2022, and studies the teaching design of "solving application problems for systems of equations". In this paper, we explore the mathematical core literacy elements contained in the teaching of solving applied problems in equations, study the improvement path of mathematical problem-solving teaching, share the teaching design practice and thinking based on core literacy oriented problem-solving teaching, and the important role that this teaching design can play in cultivating students' core literacy .

Integration of Mathematics History into Junior Middle School Education: A Pedagogical Approach to Enhance Mathematical Literacy

The integration of the history of mathematics into junior middle school mathematics education represents a significant focus of international research in mathematics and education. The mathematics curriculum standards for compulsory education have emphasized the importance of incorporating the history of mathematics, aiming to gradually integrate it into the mathematics classroom. However, in the practical implementation of junior middle school mathematics education, the effective combination of the history of mathematics with teaching methodologies remains largely unexplored. This article explores the integration of junior middle school mathematics education and the history of mathematics, aiming to provide classroom teaching recommendations for teachers and promote the formation of students’ mathematical literacy.

Reflection on Implementing Data Concept in the Junior High School Mathematics Classroom

As one of the core literacy proposed by the Mathematics Curriculum Standards for Compulsory Education (2022 Edition), the implementation of the data concept in the current junior high school mathematics classrooms has attracted much attention in China. This paper used the method of theoretical research, through in-depth and systematic analysis of the meaning of data concept literacy in curriculum standards and the requirements for junior high school students, through literature review, in-depth and systematic analysis and induction of the current teaching situation, as the theoretical basis of this study, four suggestions were put forward: 1. Design implementable statistical activities; 2. Focus on summarizing the similarities and differences and characteristics of data analysis methods; 3. Use of multimedia emerging technologies to assist teaching effectively; 4. Design the topic of probability to carry out special training, hoping to provide ideas for better development of junior high school mathematics teaching.

Reconstruction of the Mathematics Classroom Teaching System under the New Curriculum Philosophy—Analysis Based on Compulsory Mathematics Curriculum Standards (2022)

Reconstruction of the Mathematics Classroom Teaching System under the New Curriculum Philosophy—Analysis Based on Compulsory Mathematics Curriculum Standards (2022)

Examining the Integration of Model Concept Literacy in Mathematics Instruction for Junior High School Students

Compulsory Education Mathematics Curriculum Standards [1] emphasizes the core literacy of model concept, and there are many current studies around model concept, but there are few analyses aimed at the implementation of the model concept literacy of the junior high school mathematics curriculum standard in the junior high school mathematics classroom teaching, so this paper analyzes the feasibility of and strategies for the implementation of the model concept based on the connotation of the model concept and the current status quo of junior high school mathematics teaching. Teachers can take the form of collective lesson planning to strengthen the understanding of the connotation of the model concept; introduce the materials related to mathematical learning that occurs in real life into the classroom promptly, and show them to students in the classroom in a contextual way; explain the process of mathematical modeling, knowledge points, analytical ideas, and other basic knowledge, and use a variety of teaching methods such as inspirational, discursive, exploratory, and practical, to create a relaxed and free learning atmosphere; promote students' mastery of equations, inequalities, functions, and other knowledge, creating opportunities to cultivate model concept literacy, consciously carrying out practical teaching activities, improving the ability to use mathematical models to solve problems, etc., to be able to truly implement the model concept in the classroom.

Reflection on Implementing Geometric Intuition in the Junior High School Mathematics Classroom

As one of the core literacies emphasized in the Mathematics Curriculum Standards for Compulsory Education (2022 Edition), geometric intuition has been widely valued in the current junior high school mathematics teaching. Based on the method of theoretical analysis, this paper analyzes the connotation of geometric intuition literacy combines it with the practice of current mathematics classroom teaching, and proposes four implementation strategies for geometric intuition literacy in junior high school mathematics classrooms, which are as follows: 1. Add operational practice to classroom teaching; 2. Provide thematic courses related to ruler drawing; 3. Reasonable use of modern educational technology to assist classroom teaching; 4. Organize special questions about charts to practice with students. These strategies can be used for reference by junior high school mathematics teachers in practical teaching.

Analysis of Operation Ability Literacy in Junior Middle School Mathematics Classroom Teaching

The "Compulsory Education Mathematics Curriculum Standards (2022 Edition)" revised in 2022 clearly points out that the cultivation of mathematical operation ability is of great significance and value to the development of students' core literacy. Starting from the analysis of the connotation and requirements of mathematical operation ability literacy in the new curriculum standard, this paper analyzes the current situation of implementing mathematical operation ability literacy in the current junior middle school mathematics classroom teaching. Therefore, specific suggestions are put forward for the implementation of operation ability literacy: 1. Teachers should pay attention to the introduction in class and students' mastery of algorithms and calculation laws; 2. Teachers should standard their own problem-solving process to play an exemplary role; 3. Teachers should emphasize the principle of operation so as to encourage the students to make simple calculations; 4. In the teaching process, teachers should pay attention to guiding and questioning students, so as to promote the development of students' mathematical reasoning ability. These strategies can provide a reference for junior middle school mathematics teachers to cultivate students' mathematical operation abilities.

The Journey Continues: Mathematics Curriculum Analysis from the Official Curriculum to the Intended Curriculum

In this paper, we share major lessons we have learned in our curriculum analysis explorations and provide suggestions for future mathematics curriculum research. Specifically, we will discuss the successes and challenges of using comparative methods and developing analytical frameworks. Using an old Chinese saying, follow the vine to get the melon (顺藤摸瓜), our journey starts with getting a holistic picture of standards and moves to identifying a specific topic in the textbooks. We first conducted a study to compare the geometry standards of the Common Core State Standards for Mathematics (CCSSM) and the Chinese Compulsory Education Mathematics Curriculum Standards (CMCS); then we analyzed the presentation of a specific topic, triangle congruence, in multiple geometry textbooks. For each comparative study we conducted, developing the analytical framework that can be used to guide future investigations constituted a critical step in the research methodology. We have learned lessons from adapting the well-known van Hiele model, which was created for the development of geometric reasoning, into a lens for a detailed curriculum analysis. We have also learned lessons from elaborating on the key constructs from the “Mathematics Curriculum as Story” framework for coding and analysis. These lessons as well as our future directions serve as the primary focus of this paper.

Research on the Implementation of Space Concept Literacy in the Junior High School Mathematics Classroom Teaching in China

Current junior high school mathematics classrooms are increasingly focusing on the implementation of mathematics core literacy in China. Space concept literacy is one of the core literacy, so its implementation is attracting much attention. Based on clarifying the connotation and requirements of space concept literacy in the Mathematics Curriculum Standards for Compulsory Education (2022 Edition), and analyzing the highlights and deficiencies of junior high school mathematics classroom teaching, this paper puts forward four strategies for the implementation of space concept literacy in the classrooms: 1. designing life-related geometric inquiry activities with clear programs; 2. making reasonable use of objects and models; 3. adding measurement, graphing, manipulation into the teaching process; 4. flexibly using mathematics teaching software and emerging technologies to assist teaching. It is hoped that these strategies can provide ideas for the better development of junior high school mathematics teaching.

Research on Pre-employment Junior High School Mathematics Teachers' Perceptions of Model Concept Literacy in China

At present, the educational problem of model concept literacy of students in compulsory education has become one of the focuses of attention in China, and many scholars have conducted research on it, but there are fewer studies on the cognitive level of model concept literacy of pre-employment teachers, and there is still a research gap. In this study, 20 graduate students majoring in subject teaching mathematics and undergraduates who have been admitted to this specialty in a university were surveyed, and the open-ended interview method was used to investigate the model concept literacy of pre-employment teachers. The analysis of the data revealed that (1) the depth of pre-employment teachers' knowledge of model concept is shallow and remains concentrated at a low level, especially with regard to the concept of model concept and the requirements that students need to meet; (2) the depth of pre-employment teachers' knowledge of the model concept was shallow and still concentrated at a low level; and (3) the clarity of pre-employment teachers' knowledge of the model concept was low, few teachers clearly recognize the points in Compulsory Education Mathematics Curriculum Standards(2022 edition), and they either did not have a full understanding of the model concept or did not have a good understanding of the model concept. Therefore, it is recommended that: (1) pre-employment teachers should have an all-round understanding of the model concept and related contents; (2) they should have an in-depth understanding of the requirements and meanings of model concept at different levels; and (3) they should be able to clearly and accurately articulate the requirements of the Compulsory Education Mathematics Curriculum Standards (2022 edition) and put them into practice.

Research on Mathematics Expression Ability among Chinese High School Students

Mathematics expression ability is of great significance to the development of students' logical thinking. It is an essential ability required in the new mathematics curriculum standards, and it is also the focus of the current high school entrance examination and National College Entrance examination. This study used the China National Knowledge Internet (CNKI) as a data source to summarize and sort out previous research in order to provide suggestions for current teaching and found that: (1) Current domestic research on mathematics expression ability of high school students mainly focuses on the following five aspects: connotations and classification of mathematics expression ability, development status of mathematics expression ability, evaluation frameworks of mathematics expression ability, strategies for cultivating students' mathematics expression ability, and the mathematics expression ability of special groups of students. (2) There is relatively little research on the evaluation frameworks and influencing factors of mathematics expression ability, and most training strategies focus on how teachers teach, with very few on how students learn. Previous researchers use self-made test papers, questionnaires or interview outlines to investigate and research, and some researchers base their research on theoretical thinking or teaching experience. (3) Therefore, based on current research, future research needs to adopt more scientific research tools, a more reasonable analysis framework, expand the research scope, increase validation research, and give more scientific suggestions. So that the research on the mathematics expression ability of high school students is more comprehensive, systematic, and profound.

Effect of Model-Based Problem Solving on Error Patterns of At-Risk Students in Solving Additive Word Problems

Students with learning disabilities/difficulties in mathematics often apply ineffective procedures to solve word problems due to a lack of conceptual understanding of word problem solving, which results in poor mathematics performance and falling further behind the normal achievements of their peers. Current mathematics curriculum standards emphasize conceptual understanding in problem solving as well as higher-order thinking and reasoning, including all students. The purpose of this study was to evaluate the impact of a computer-assisted model-based problem-solving intervention program (MBPS) on elementary students’ word problem-solving performance by analyzing the error patterns. Results indicate that after the MBPS intervention, participants significantly improved their problem-solving performance and made fewer errors in solving problems across a range of additive word problem situations. Specifically, the participating students made their attempt to represent the mathematical relation, decontextualized from the word problem story, in the model equation before solving the problem, rather than blindly applying an operation or relying on the “keyword” strategy as they did during the preassessment. Implications of the study are discussed in the context of the National Council of Teachers of Mathematics’ calling for teaching big ideas to help students develop a deep understanding of mathematics knowledge.

The Research on Middle School Mathematics Teaching Based on BOPPPS Model -- Taking the Teaching Design of "Determination of Congruent Triangles" as an Example

The Mathematics Curriculum Standards for Compulsory Education (2022 Edition) places higher demands on junior high school mathematics teaching, emphasizing students' active participation in classroom activities and the development of core literacies, mobilizing students' interest in learning as much as possible, fostering students' initiative and enthusiasm for learning, and making students the masters of the classroom, with the teacher merely a "guide" of knowledge, returning the classroom to the students. The BOPPPS model is a teaching model in which students participate in all aspects as well as play an important role in teaching objectives. Applying this model in middle school mathematics teaching can help teachers improve teaching efficiency and also increase the proportion of students' participation in the classroom. In this study, this model is applied to the design of middle school mathematics teaching, and the first lesson of "Determination of congruent triangles" is used as a case study for analysis. Through the introduction of real-life scenarios, specific and testable classroom objectives, review of old knowledge as a pre-assessment, active and participatory learning of students, post-test of the content in the classroom, and summary and self-evaluation of students, students can experience the process of knowledge occurrence and development, establish a systematic knowledge system of the content, develop students' core literacy, improve the teaching efficiency of the classroom, and provide a new direction for teachers to think about their teaching.

데이터 리터러시 관점에서 초등 수학과 성취기준 및 교과서 문제의 비구조성(ill-structured) 비교분석

Objectives The purposes of this study were to analyze the achievement standards of elementary mathematics and curriculum in each country from the perspective of data literacy, compare and analyze the problem of ill-structured in math textbooks, and present the direction of future curriculum and textbook development.
 Methods To analyze the elementary mathematics curriculum standards in Korea, the United States, Japan, and India from a data literacy perspective, components of data literacy was selected and analyzed with a focus on whether the standards in each country's curriculum reflect the content of the components. After categorizing the standards, to analyze the cognitive level of the standards, the level of the standards is compared by the mathematics cognitive domain, which is an indicator for the development of the TIMSS 2019 assessment, and the problems ill-structured of in each country are examined in terms of realism, complexity, and openness.
 Results Compared to other countries, Korea did not deal with various aspects of data literacy in the curriculum standards, and showed a low proportion in the cognitive domain that requires high-dimensional thinking. The problems of ill-structured in textbook were practical in that it mimics the real situation and provides descriptions and information about the situation, but complexity and openness were relatively not revealed, confirming the need to develop meaningful textbook problems for learners in the future.
 Conclusions In the curriculum, it is necessary to emphasize various aspects and high-dimensional thinking on the perspectives and components of data literacy and to be guided in connection with ‘data ethics’. Mathematics textbooks should be able to utilize high-dimensional thinking skills through ill-structured status and aspects of practicality, complexity, and openness need to be systematically presented. Pre-service teachers and teachers also suggested that the development of training and programs to foster data literacy capabilities, cultivate background knowledge on ill-structured status, and support teaching and learning design be conducted as follow-up studies.

Research on the Mathematics Space Concept of Junior High School Students in China

The space concept is one of the main manifestations of the mathematics core competencies in the compulsory education stage as required by the Mathematics Curriculum Standards for Compulsory Education (2022 edition). In the past two decades, many scholars have studied the space concept, but there is no literature to systematically summarize the research results. Therefore, this paper adopts the literature analysis method to review 47 papers related to the mathematics space concept of junior high school students in China, and obtains the following conclusions: After the promulgation of the Mathematics Curriculum Standards for Compulsory Education (2022 edition), the research on the space concept has increased, but it is mostly theoretical research and less empirical research. The research is divided into six aspects: the connotation and components of the space concept, the division of the space concept's dimensions, the current development status of the space concept of junior high school students, factors influencing the space concept, ways to cultivate the space concept, and curriculum resources development. Studies on the dimensional division, the current development status, and the ways of cultivating the space concept are abundant. The division of dimensions and levels of the space concept provides a research approach to further understanding the development status of junior high school students. The research on the development status suggests that teachers should analyze the weak points in the space concept combined with the specific situation of students. The research on the cultivation ways innovates the design of teachers' teaching activities. But these studies all focus on the period before the promulgation of the new edition standards. There is a lack of research on the connotation and components, the influencing factors, and the development of curriculum resources. Therefore, it is necessary to analyze the research week's points further. The space concept can be interpreted from different perspectives in conjunction with other related disciplinary theories, the influence factors such as students' pre-preparation and teachers' teaching styles can be examined, and a variety of in-school and out-of-school resources and networked resources can be flexibly applied for curriculum development.

Development Paths of Senior High School Students’ Mathematical Modeling Capability Based on Core Literacy

Mathematical core literacies centrally reflect the curriculum goals of mathematics, and are acquired and developed by students when studying and applying mathematics. Mathematical modeling, a part of core literacies and an essential capability for senior high school students, is critical to their innovative practice and deep learning. The new mathematics curriculum standards have included mathematical modeling as core literacy and China’s college entrance exam has started to highlight the applied nature of mathematics. However, equal stress fails to be laid on mathematical modeling in math class. Against such a background, this paper specifies the importance, and summarizes the current challenges alongside paths of developing mathematical modeling capability.

Implementation of Model Concept of Core Literacy in Mathematics in China

Compulsory Education Mathematics Curriculum Standards (2022 edition) puts forward the core literacy of the model concept. There are now many studies that concentrate on the model concept, but there are seldom any thorough generalized studies on this topic. The following results are reached by adopting the method of literature analysis to synthesize the pertinent research literature on the model idea in China: (1) The current research on the model concept at the compulsory education level has a very broad scope and includes in-depth investigations on the model concept's status, significance, the classroom design, and penetration strategies of model concept. (2) Most studies are conducted in terms of curricular content and subjects, and they focus on a limited number of fixed themes, such as quadratic equations, quadratic inequalities, and functions. To demonstrate how to fully understand the model concept, researchers offer practical examples and instructional designs. (3) But in terms of curricular styles, there aren't many studies on the model concept. To strengthen the research content, encourage in-depth study by academics and front-line instructors, and increase the effectiveness of the model concept's penetration, it is required to extend the research direction and the entry point.

Research on Relationship of Mathematical Literacy in Mathematics Curriculum Standards and Evaluation in Higher Vocational Education

The relationship between higher vocational mathematics curriculum standards and core literacy is analyzed as it is of great significance for discussing the reform of higher vocational mathematics curricula for the cultivation of core literacy. The information resource data related to the curriculum standard is processed through the literature method and content analysis method. As a result, the existing mathematical classification and characteristics of higher vocational education are investigated with mathematical models. In the PSIA evaluation framework, the relationship between curriculum standards and mathematical literacy is evaluated and studied.